Those "What are these boards" are the ERR RailSounds Commander prior to the new single board design. The top board is a generic Railsounds 4 sound board and the bottom board is the motherboard and power supply replacement. The new RS Commander is a single board unit that also uses the RailSounds 5 technology and offers better sound.
I'd try adding a battery, it plugs into the bottom board of that pair. I've added the manual to this post.
You can try reseating all the connectors as well as the chips in the RailSounds board, that's a frequent issue with intermittent sound.
As far as the "avoid the wire, you can connect that wire under the bottom of the motherboard on the matching connector. That's supplying 5 volts for an IR tether, though I didn't know 3rd Rail did those. In any case, the yellow wire is supplying 5 volts for something.
The card with the heatsink is the Cruise Commander, the R2LC plugs into it. I'm amazed that ERR told you that was the sound board was the Cruise Commander, and frankly I think you misunderstood what they were saying.
For better sound, I'd also replace that anemic speaker!
